GCF of 757/306, 512/538
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 757/306, 512/538 i.e 1/82314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 757/306, 512/538.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 757/306,512/538?
Given fractions are 757/306,512/538
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 757/306,512/538, numerators are 757,512
Denominators are 306,538
The GCF of 757,512 is 1 .
LCM of 306,538 is 82314.
The greatest common factor of 757/306,512/538 = [GCF of 757,512]/[LCM of 306,538]= 1/82314
Therefore, the GCF of 757/306,512/538 is 1/82314.
To find the highest common factor of 757,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 757 are 1, 757
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 757,512 is 1.
Lets's calculate GCF of 757,512
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 757,512 By Matching Biggest Common Factor Method
Now, list down the factors of 757
:1,757
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 757,512 . The biggest common factor number is the GCF number.
So the greatest common factor 757,512 is 1.
Lets's calculate LCM of 306,538
| 2 | 306, 538 |
| 153, 269 |
∴ So the LCM of the given numbers is 2 x 153 x 269 = 82314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82314
Therefore, the GCF of Fractions 757/306,512/538 is 1/82314
Least Common Multiple of 306,538 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 306,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,538) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(306,538) x common factors =2 x 1 = 2
LCM(306,538) = ( 306 × 538 ) / 2
LCM(306,538) = 164628 / 2
LCM(306,538) = 82314
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FAQs on GCF of Fractions of 757/306, 512/538
1. What is the HCF of 757,512?
The HCF of 757,512 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 757/306, 512/538?
Answer: GCF of Numerators as per given numbers 757/306, 512/538 is
GCF of Numerators i.e. for 757,512 is 1
LCM of denominators i.e. for 306,538 is 82314.
Thus, GCF of Fractions is 1/82314.Finally, GCF of Fractions for 757/306, 512/538 is 1/82314.